People on a Line

AtCoder

IDarc090_b

Time2000ms

Memory256MB

Difficulty—

There are $N$ people standing on the $x$\-axis. Let the coordinate of Person $i$ be $x_i$. For every $i$, $x_i$ is an integer between $0$ and $10^9$ (inclusive). It is possible that more than one person is standing at the same coordinate. You will given $M$ pieces of information regarding the positions of these people. The $i$\-th piece of information has the form $(L_i, R_i, D_i)$. This means that Person $R_i$ is to the right of Person $L_i$ by $D_i$ units of distance, that is, $x_{R_i} - x_{L_i} = D_i$ holds. It turns out that some of these $M$ pieces of information may be incorrect. Determine if there exists a set of values $(x_1, x_2, ..., x_N)$ that is consistent with the given pieces of information. ## Constraints * $1 \leq N \leq 100$ $000$ * $0 \leq M \leq 200$ $000$ * $1 \leq L_i, R_i \leq N$ ($1 \leq i \leq M$) * $0 \leq D_i \leq 10$ $000$ ($1 \leq i \leq M$) * $L_i \neq R_i$ ($1 \leq i \leq M$) * If $i \neq j$, then $(L_i, R_i) \neq (L_j, R_j)$ and $(L_i, R_i) \neq (R_j, L_j)$. * $D_i$ are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $L_1$ $R_1$ $D_1$ $L_2$ $R_2$ $D_2$ $:$ $L_M$ $R_M$ $D_M$ [samples]

Samples

Input #1

Output #1

Yes

Some possible sets of values $(x_1, x_2, x_3)$ are $(0, 1, 2)$ and $(101, 102, 103)$.

Input #2

Output #2

No

If the first two pieces of information are correct, $x_3 - x_1 = 2$ holds, which is contradictory to the last piece of information.

Input #3

Output #3

Yes

Input #4

Output #4

No

Input #5

100 0

Output #5

Yes

API Response (JSON)

{
  "problem": {
    "name": "People on a Line",
    "description": {
      "content": "There are $N$ people standing on the $x$\\-axis. Let the coordinate of Person $i$ be $x_i$. For every $i$, $x_i$ is an integer between $0$ and $10^9$ (inclusive). It is possible that more than one pers",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc090_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ people standing on the $x$\\-axis. Let the coordinate of Person $i$ be $x_i$. For every $i$, $x_i$ is an integer between $0$ and $10^9$ (inclusive). It is possible that more than one pers...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments